{"author_name":"atcoder","url":"https://info.atcoder.jp/entry/algorithm_lectures/sperner_theorem","published":"2026-05-01 11:15:02","blog_title":"AtCoderInfo","provider_url":"https://hatena.blog","type":"rich","width":"100%","height":"190","title":"Sperner \u306e\u5b9a\u7406","provider_name":"Hatena Blog","categories":["\u9806\u5e8f\u96c6\u5408","Sperner \u306e\u5b9a\u7406","LYM \u4e0d\u7b49\u5f0f","Dilworth \u306e\u5b9a\u7406","\u30de\u30c3\u30c1\u30f3\u30b0"],"html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Finfo.atcoder.jp%2Fentry%2Falgorithm_lectures%2Fsperner_theorem\" title=\"Sperner \u306e\u5b9a\u7406 - AtCoderInfo\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","author_url":"https://blog.hatena.ne.jp/atcoder/","blog_url":"https://info.atcoder.jp/","description":"\u89e3\u8aac\u52d5\u753b\u306f\u3053\u3061\u3089\u3067\u3059\uff0e 1. \u6982\u8981 \u672c\u8a18\u4e8b\u3067\u306f\uff0c\u30d6\u30fc\u30eb\u675f $B_n$ \u306b\u304a\u3051\u308b\u53cd\u9396\u306e\u6700\u5927\u30b5\u30a4\u30ba\u3092\u4e0e\u3048\u308b Sperner \u306e\u5b9a\u7406\u3092\u89e3\u8aac\u3057\u307e\u3059\uff0e Sperner \u306e\u5b9a\u7406\u306f\uff0c\u96c6\u5408 $\\lbrace 0,1,\\dots,n-1\\rbrace$ \u306e\u90e8\u5206\u96c6\u5408\u3092\uff0c\u3069\u306e $2$ \u3064\u3082\u4e92\u3044\u306b\u5305\u542b\u95a2\u4fc2\u304c\u306a\u3044\u3088\u3046\u306b\u9078\u3076\u3068\u304d\u306b\uff0c\u9078\u3079\u308b\u90e8\u5206\u96c6\u5408\u306e\u500b\u6570\u306e\u6700\u5927\u5024\u304c $$ \\binom{n}{\\lfloor n/2\\rfloor} $$ \u3067\u3042\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3059\u308b\u5b9a\u7406\u3067\u3059\uff0e\u672c\u8a18\u4e8b\u3067\u306f\u3053\u306e\u5b9a\u7406\u306b\u3064\u3044\u3066 $2$ \u901a\u308a\u306e\u8a3c\u660e\u3092\u4e0e\u3048\uff0c\u7b49\u53f7\u6210\u7acb\u6761\u4ef6\u3084\u3044\u304f\u3064\u304b\u306e\u95a2\u9023\u4e8b\u9805\u306b\u3064\u3044\u3066\u3082\u89e3\u8aac\u3057\u307e\u3059\uff0e\u3053\u308c\u3089\u306e\u8b70\u8ad6\u306f\uff0c\u9396\u3084\u53cd\u9396\u3068\u3044\u3063\u305f\u9806\u5e8f\u96c6\u5408\u306b\u304a\u3051\u308b\u91cd\u8981\u2026","version":"1.0","image_url":"https://img.atcoder.jp/aal-image-library/f0cf88f1bb6fe416aa8129961a0e3140.png"}